Arranging combinations

I have 14 numbers I want to combine in sets of 3 numbers in such a way no 2 numbers appear together 2 or more times in a set.
Obviously as you have to combine each value with 2 others to make a set there will be ONE number that will NOT be combined with a certain number. I want each number to be not-combined just 1 time.

I have made a program that calculates all but ONE of the (28) combinations but can't find a solution to create them all.

If possible i would like to have an algorithm (or better : program) to CALCULATE (not search in a list of elements) that arranges the 'uncombined numbers' on a diagonal (so : 1--> 14 ; 2-->13 ; 3-->12 etc not combined) or 'next to each other' (so : 1--> 2; 3-->4; 5-->6 etc not combined)